ProfHewitt

8 ms·

31.
by ProfHewitt 5y ago
Messages themselves should be Actors.
32.
by ProfHewitt 5y ago
Excellent video by Dan Ingalls on the Xerox early history of Smalltalk. In November 1972, Alan Kay gave an inspiring seminar at MIT on Smalltalk-72. There were ongoing discussions during the weeks after the lecture about the following:
33.
by ProfHewitt 5y ago
It's useful enough to have gained an effective monopoly. However, it cannot be relied upon in specific instances.
34.
by ProfHewitt 5y ago
Unfortunately, Wikipedia is often not a reliable source of information because its articles are posted and maintained by largely unaccountable anonymous parties.
35.
by ProfHewitt 5y ago
Dear Jørgen Veisdal: Fair enough. But it would be helpful if the article could be updated to get some information corrected as pointed out in other posts on this page.
36.
by ProfHewitt 5y ago
History of the people involved is indeed very interesting. Particularly recommend the BBC2 film "Dangerous Knowledge". BTW: The article "Turing Uncomputability" got some of the history wrong about the 1930 interaction b
37.
by ProfHewitt 5y ago
The [Church 1935] proof of the computational undecidability of the halting problem is essentially the same as the [Turing 1936] proof. Consequently, the article under discussion would be better titled "Church/Turing Uncomputabili
38.
by ProfHewitt 5y ago
Unfortunately, the article "Turing Uncomputability" is incorrect that [Gödel, 1931] was first to prove inferential undecidablity of mathematical foundations. The [Gödel, 1931] proof using the proposition I'mUnprovable is
39.
by ProfHewitt 5y ago
The Church/Turing Hypothesis is false because there are digital computations that cannot be performed by a Nondeterministic Turing Machine . For example, see the following: https://papers.ssrn.com/abstract=3603021
40.
by ProfHewitt 5y ago
"Event-driven architecture" only considers a small subset of the computational events fundamental to understanding computation. Actor Theory is based on automatizing the "precedes" partial order for all computational e
41.
by ProfHewitt 5y ago
Sets initially seemed appealing because they are less abstract than types. However, the lack of abstraction turned out to be a fatal flaw in attempts to make sets the foundations of mathematics because: * sets cannot be rigorously def
42.
by ProfHewitt 5y ago
BoiledCabbage: You are on the right track! [Dedekind 1888] started out on the correct path by defining natural numbers up to a unique isomorphism. Unfortunately, there was long detour through 1st-order logic :-( Powerful foundations are now
43.
by ProfHewitt 5y ago
Orthodoxy in science works until the next paradigm shift. See "In retrospect: The Structure of Scientific Revolutions" https://www.nature.com/articles/484164a
44.
by ProfHewitt 5y ago
Unfortunately, 1st-order ZFC has very severe limitations because it does not precisely define sets. However, ordinals that provide the backbone of sets have been precisely defined up to a unique isomorphism using types. See the following ar
45.
by ProfHewitt 5y ago
Types are about rigorously constructing mathematical abstractions from primitive types defined up to a unique isomorphism. In fact, types have become the primary foundation of Computer Science. Russell introduced the crucial concept of the
46.
by ProfHewitt 5y ago
Note that forcing and the independence results are only for 1st-order logic . They do not work for theories that characterize mathematical abstractions such as the Ordinals and Natural Numbers up to a unique isomorphism. See the followin
47.
by ProfHewitt 5y ago
Lawvere's work is elegant! However, Lawvere missed the crucial importance of Russell's orders on propositions in blocking the construction of monster propositions using recursive definitions . Orders on propositions block constru
48.
by ProfHewitt 5y ago
PS. There are no ordinals of intermediate cardinality between ω<sub>0</sub> and ω<sub>1</sub>.
49.
by ProfHewitt 5y ago
The results in the article are based on 1st-order logic, which is inadequate for the foundations of mathematics. Mathematical abstractions need to be characterized up a unique isomorphism as in the theory Ordinals described in the following
50.
by ProfHewitt 5y ago
Unfortunately, a theoretical embedding doesn't always accomplish the work of Double Negation Elimination in practice.
51.
by ProfHewitt 5y ago
Constructivism is based on intuitionistic logic, which lacks some important logical principles. For example, it lacks the following principles: * excluded middle * double negation elimination The principles can be valuable f
52.
by ProfHewitt 5y ago
The Howard-Curry correspondence does not help proving properties of concurrent systems. Instead, need to use Actor Event induction: https://papers.ssrn.com/abstract=3418003
53.
by ProfHewitt 5y ago
Foundations of mathematics are inferentially incomplete, that, is, there are true but unprovable propositions (although [Gödel 1934] results do not hold for foundations). See following for a proof: https://papers.ssrn.com/
54.
by ProfHewitt 5y ago
Joker_vD: Looks like you are incorrect because Func and FuncToFunc are defined recursively.
55.
by ProfHewitt 5y ago
Is FuncToFunc defined recursively in the excerpt below??? private static interface FuncToTFunc<T> { Func<T> apply(FuncToTFunc<T> x); } BTW, what is "x" in the above? Also is Func define
56.
by ProfHewitt 5y ago
Does the github Java code make use of recursion?
57.
by ProfHewitt 5y ago
Thanks! Could you use your Java code to define Factorial?
58.
by ProfHewitt 5y ago
Could you write this in Java?
59.
by ProfHewitt 5y ago
Y Combinator does not work for strongly-typed programs because the definition is not strongly typed. Instead recursion must be added as an additional primitive to the lambda calculus. See https://papers.ssrn.com/abstract=3
60.
by ProfHewitt 5y ago
Classical mathematical logic requires complete consistency. Discourse using empirical information inevitably involves some disagreement requiring robust inference. See the following article: https://papers.ssrn.com/abstract=

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